Solve for x 36x^2-12x+1=0

$36 x^{2} - 12 x + 1 = 0$

Step 1

Factor using the perfect square rule.

Rewrite $36 x^{2}$ as ${(6 x)}^{2}$ .

${(6 x)}^{2} - 12 x + 1 = 0$

Rewrite $1$ as $1^{2}$ .

${(6 x)}^{2} - 12 x + 1^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$12 x = 2 \cdot (6 x) \cdot 1$

Rewrite the polynomial.

${(6 x)}^{2} - 2 \cdot (6 x) \cdot 1 + 1^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 6 x$ and $b = 1$ .

${(6 x - 1)}^{2} = 0$

Step 2

Set the $6 x - 1$ equal to $0$ .

$6 x - 1 = 0$

Step 3

Solve for $x$ .

Add $1$ to both sides of the equation.

$6 x = 1$

Divide each term in $6 x = 1$ by $6$ and simplify.

Divide each term in $6 x = 1$ by $6$ .

$\frac{6 x}{6} = \frac{1}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{1}{6}$

Divide $x$ by $1$ .

$x = \frac{1}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{6}$

Decimal Form:

$x = 0.1\overline{6}$